Network Models and Simulation Analytics for Multi-scale Dynamics of Biological Invasions.

Globalization and climate change facilitate the spread and establishment of invasive species throughout the world via multiple pathways. These spread mechanisms can be effectively represented as diffusion processes on multi-scale, spatial networks. Such network-based modeling and simulation approaches are being increasingly applied in this domain. However, these works tend to be largely domain-specific, lacking any graph theoretic formalisms, and do not take advantage of more recent developments in network science. This work is aimed toward filling some of these gaps. We develop a generic multi-scale spatial network framework that is applicable to a wide range of models developed in the literature on biological invasions. A key question we address is the following: how do individual pathways and their combinations influence the rate and pattern of spread? The analytical complexity arises more from the multi-scale nature and complex functional components of the networks rather than from the sizes of the networks. We present theoretical bounds on the spectral radius and the diameter of multi-scale networks. These two structural graph parameters have established connections to diffusion processes. Specifically, we study how network properties, such as spectral radius and diameter are influenced by model parameters. Further, we analyze a multi-pathway diffusion model from the literature by conducting simulations on synthetic and real-world networks and then use regression tree analysis to identify the important network and diffusion model parameters that influence the dynamics.

Fundamental limitations on efficiently forecasting certain epidemic measures in network models.

The ongoing COVID-19 pandemic underscores the importance of developing reliable forecasts that would allow decision makers to devise appropriate response strategies. Despite much recent research on the topic, epidemic forecasting remains poorly understood. Researchers have attributed the difficulty of forecasting contagion dynamics to a multitude of factors, including complex behavioral responses, uncertainty in data, the stochastic nature of the underlying process, and the high sensitivity of the disease parameters to changes in the environment. We offer a rigorous explanation of the difficulty of short-term forecasting on networked populations using ideas from computational complexity. Specifically, we show that several forecasting problems (e.g., the probability that at least a given number of people will get infected at a given time and the probability that the number of infections will reach a peak at a given time) are computationally intractable. For instance, efficient solvability of such problems would imply that the number of satisfying assignments of an arbitrary Boolean formula in conjunctive normal form can be computed efficiently, violating a widely believed hypothesis in computational complexity. This intractability result holds even under the ideal situation, where all the disease parameters are known and are assumed to be insensitive to changes in the environment. From a computational complexity viewpoint, our results, which show that contagion dynamics become unpredictable for both macroscopic and individual properties, bring out some fundamental difficulties of predicting disease parameters. On the positive side, we develop efficient algorithms or approximation algorithms for restricted versions of forecasting problems.

GDSCalc: A Web-Based Application for Evaluating Discrete Graph Dynamical Systems.

Discrete dynamical systems are used to model various realistic systems in network science, from social unrest in human populations to regulation in biological networks. A common approach is to model the agents of a system as vertices of a graph, and the pairwise interactions between agents as edges. Agents are in one of a finite set of states at each discrete time step and are assigned functions that describe how their states change based on neighborhood relations. Full characterization of state transitions of one system can give insights into fundamental behaviors of other dynamical systems. In this paper, we describe a discrete graph dynamical systems (GDSs) application called GDSCalc for computing and characterizing system dynamics. It is an open access system that is used through a web interface. We provide an overview of GDS theory. This theory is the basis of the web application; i.e., an understanding of GDS provides an understanding of the software features, while abstracting away implementation details. We present a set of illustrative examples to demonstrate its use in education and research. Finally, we compare GDSCalc with other discrete dynamical system software tools. Our perspective is that no single software tool will perform all computations that may be required by all users; tools typically have particular features that are more suitable for some tasks. We situate GDSCalc within this space of software tools.

Inhibiting diffusion of complex contagions in social networks: theoretical and experimental results.

We consider the problem of inhibiting undesirable contagions (e.g. rumors, spread of mob behavior) in social networks. Much of the work in this context has been carried out under the 1-threshold model, where diffusion occurs when a node has just one neighbor with the contagion. We study the problem of inhibiting more complex contagions in social networks where nodes may have thresholds larger than 1. The goal is to minimize the propagation of the contagion by removing a small number of nodes (called critical nodes) from the network. We study several versions of this problem and prove that, in general, they cannot even be efficiently approximated to within any factor ρ ≥ 1, unless P = NP. We develop efficient and practical heuristics for these problems and carry out an experimental study of their performance on three well known social networks, namely epinions, wikipedia and slashdot. Our results show that these heuristics perform significantly better than five other known methods. We also establish an efficiently computable upper bound on the number of nodes to which a contagion can spread and evaluate this bound on many real and synthetic networks.

Dental insurance! Are we ready?

Dental insurance is insurance designed to pay the costs associated with dental care. The Foreign Direct Investment (FDI) bill which was put forward in the winter session of the Lok Sabha (2008) focused on increasing the foreign investment share from the existing 26% to 49% in the insurance companies of India. This will allow the multibillion dollar international insurance companies to enter the Indian market and subsequently cover all aspects of insurance in India. Dental insurance will be an integral a part of this system. Dental insurance is a new concept in Southeast Asia as very few countries in Southeast Asia cover this aspect of insurance. It is important that the dentists in India should be acquainted with the different types of plans these companies are going to offer and about a new relationship which is going to emerge in the coming years between dentist, patient and the insurance company.

Discovery of association rules in medical data.

Data mining is a technique for discovering useful information from large databases. This technique is currently being profitably used by a number of industries. A common approach for information discovery is to identify association rules which reveal relationships among different items. In this paper, we use this approach to analyse a large database containing medical-record data. Our aim is to obtain association rules indicating relationships between procedures performed on a patient and the reported diagnoses. Random sampling was used to obtain these association rules. After reviewing the basic concepts associated with data mining, we discuss our approach for identifying association rules and report on the rules generated.